The infinite regress
from 350 BCE Aristotle's use against infinite chains of causes and proofs
If every one of these needs another one behind it, and there is no last one, then nothing here is doing the job it was supposed to do.
- Active
- from 350 BCE
- Where
- Athens
- Status
- In use
- Tradition
- Classical procedures
What it is
A regress argument shows that a proposed account generates an endless chain of the same demand, and that the chain never delivers what was wanted. If every belief needs a further belief to justify it, and that one needs another, then no belief is ever justified — not because the chain is long, but because nothing in it ever supplies the justification.
It is a refutation by structure rather than by counterexample. Nothing about the world is appealed to at all.
How it works
Take the proposed account. Apply its own demand to the thing it just produced. Show that the demand reappears unchanged. Show that this cannot terminate, and that nothing along the way ever satisfies the demand.
The third step is where the argument is won or lost. A regress that terminates is harmless, and a regress that is infinite but where each step does part of the work is not vicious.
The form of the inference
- The account requires that every A be supported by a further A
- Any such further A is itself an A, and so requires another
- The chain cannot terminate within the account
- No member of the chain ever supplies the support required
- Therefore the account does not deliver what it promised
The argument
Proposition A guarantee is worthless unless somebody's word is good without one.
- The contract requires the builder's performance to be guaranteed by a third party.
- The client asks what secures the guarantor's performance, and is offered a second guarantor.
- The same question applies to the second guarantor with exactly the same force, and to any further one.
- If every party's word requires backing by another party's word, no party's word is ever backed, however many are added.
- So either the chain stops with someone whose performance is secured otherwise — by assets, by a bond, by regulation — or the whole arrangement provides no security at all.
Therefore A guarantee is only worth something if it terminates in something that is not itself a guarantee.
This is the epistemological regress in commercial dress. The structure that defeats infinite chains of justification is the same one that defeats infinite chains of surety, which is why foundationalism and a bond have the same shape.
What it is good for
Testing whether an account actually explains anything or merely defers the explanation. It is one of the few arguments that can refute a position without any empirical input at all.
Where it fails
It fails when the regress is not actually vicious, and telling the two apart is genuinely hard. An infinite chain of causes stretching back in time is not obviously incoherent; an infinite series of ever-smaller contributions can sum to a finite total. The argument only works if nothing in the chain does part of the job, and that has to be shown rather than assumed.
Coherentists make exactly this reply about justification: they accept that no belief has an independent foundation and deny that this leaves anything unjustified, because support runs in a web rather than a line.
Common misconceptions
That infinite means impossible. Plenty of legitimate infinities exist in mathematics and possibly in nature. What makes a regress vicious is that the demand is never met, not that the series is endless.
Where it came from
Aristotle uses it in the Posterior Analytics to argue that demonstration must rest on indemonstrable first principles, and in the Metaphysics against infinite chains of causes.
What became of it
The central argument of the foundationalist position in epistemology, and the standing problem that coherentism and infinitism were each built to answer.
Lasting influence
It generates the epistemic regress problem, the cosmological argument, the third man argument against Plato's Forms, and Bradley's regress about relations.
Why it still matters
One of the most-used argument forms in contemporary philosophy.
Put another way
Turtles all the way down, and the ground never arriving.
Texts
Aristotle, Posterior Analytics
Book I chapters 2 and 3 argue from the impossibility of infinite demonstration to the necessity of first principles.
Where to start
Read the epistemic regress problem as set out in any contemporary epistemology text, then notice the same shape in the cosmological argument.
The surprising bit
The same argument shape produces an argument for God, an argument for foundational beliefs, and an argument against Plato's theory of Forms, which suggests it is doing something structural rather than saying anything about any of those subjects.
In their own words
It is impossible to go on ad infinitum, for then there would be no first principle
Who held it
F. H. Bradley
Connections
- Relies on
- Reductio ad absurdum
- Set against
- Grounding
- Influenced
- Sufficient reason
- Parallel to
- Grounding
The verdict
A powerful structural refutation whose force depends entirely on a distinction — vicious or benign — that has never been drawn cleanly.